Rabbits can be found in tall grass by leaving piles of carrots on the ground nearby. It seems to work best if you move far enough away so that you can just barely see the carrots, and check back every 15-20 minutes. If you are lucky you will find some of the carrots missing and a small white rabbit or two nearby. You need both a male and a female rabbit in order to breed more. It is usually much easier for new players to trade for a pair of breeding rabbits from an established player, rather than using this method to find their own.
Rabbits breed very quickly, so keep an eye on them. If they run out of carrots, they will escape the hutch. They will also escape, if there are too many in the hutch. Exactly how many that is is not known, but the number is bigger than 30.
Pluribus has verified that rabbit catching does work post-Safari (and the bunnies spawned this way don't get eaten by Falcons - this is only triggered by dropped bunnies).